Trigonometry Examples

Solve for x (3+2i)*(x+iy)=i(x-iy)+4
Step 1
Simplify .
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Step 1.1
Rewrite.
Step 1.2
Simplify by adding zeros.
Step 1.3
Expand using the FOIL Method.
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Step 1.3.1
Apply the distributive property.
Step 1.3.2
Apply the distributive property.
Step 1.3.3
Apply the distributive property.
Step 1.4
Simplify each term.
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Step 1.4.1
Multiply .
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Step 1.4.1.1
Raise to the power of .
Step 1.4.1.2
Raise to the power of .
Step 1.4.1.3
Use the power rule to combine exponents.
Step 1.4.1.4
Add and .
Step 1.4.2
Rewrite as .
Step 1.4.3
Multiply by .
Step 2
Simplify each term.
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Step 2.1
Apply the distributive property.
Step 2.2
Multiply .
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Step 2.2.1
Raise to the power of .
Step 2.2.2
Raise to the power of .
Step 2.2.3
Use the power rule to combine exponents.
Step 2.2.4
Add and .
Step 2.3
Simplify each term.
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Step 2.3.1
Rewrite as .
Step 2.3.2
Multiply by .
Step 2.3.3
Multiply by .
Step 3
Move all terms containing to the left side of the equation.
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Step 3.1
Subtract from both sides of the equation.
Step 3.2
Subtract from .
Step 3.3
Multiply by .
Step 4
Move all terms not containing to the right side of the equation.
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Step 4.1
Subtract from both sides of the equation.
Step 4.2
Add to both sides of the equation.
Step 4.3
Add and .
Step 5
Factor out of .
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Step 5.1
Factor out of .
Step 5.2
Factor out of .
Step 5.3
Factor out of .
Step 6
Divide each term in by and simplify.
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Step 6.1
Divide each term in by .
Step 6.2
Simplify the left side.
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Step 6.2.1
Cancel the common factor of .
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Step 6.2.1.1
Cancel the common factor.
Step 6.2.1.2
Divide by .
Step 6.3
Simplify the right side.
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Step 6.3.1
Simplify terms.
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Step 6.3.1.1
Simplify each term.
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Step 6.3.1.1.1
Multiply the numerator and denominator of by the conjugate of to make the denominator real.
Step 6.3.1.1.2
Multiply.
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Step 6.3.1.1.2.1
Combine.
Step 6.3.1.1.2.2
Simplify the numerator.
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Step 6.3.1.1.2.2.1
Apply the distributive property.
Step 6.3.1.1.2.2.2
Multiply by .
Step 6.3.1.1.2.2.3
Multiply by .
Step 6.3.1.1.2.3
Simplify the denominator.
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Step 6.3.1.1.2.3.1
Expand using the FOIL Method.
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Step 6.3.1.1.2.3.1.1
Apply the distributive property.
Step 6.3.1.1.2.3.1.2
Apply the distributive property.
Step 6.3.1.1.2.3.1.3
Apply the distributive property.
Step 6.3.1.1.2.3.2
Simplify.
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Step 6.3.1.1.2.3.2.1
Multiply by .
Step 6.3.1.1.2.3.2.2
Multiply by .
Step 6.3.1.1.2.3.2.3
Multiply by .
Step 6.3.1.1.2.3.2.4
Multiply by .
Step 6.3.1.1.2.3.2.5
Raise to the power of .
Step 6.3.1.1.2.3.2.6
Raise to the power of .
Step 6.3.1.1.2.3.2.7
Use the power rule to combine exponents.
Step 6.3.1.1.2.3.2.8
Add and .
Step 6.3.1.1.2.3.2.9
Add and .
Step 6.3.1.1.2.3.2.10
Add and .
Step 6.3.1.1.2.3.3
Simplify each term.
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Step 6.3.1.1.2.3.3.1
Rewrite as .
Step 6.3.1.1.2.3.3.2
Multiply by .
Step 6.3.1.1.2.3.4
Add and .
Step 6.3.1.1.3
Factor out of .
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Step 6.3.1.1.3.1
Factor out of .
Step 6.3.1.1.3.2
Factor out of .
Step 6.3.1.1.3.3
Factor out of .
Step 6.3.1.1.4
Multiply the numerator and denominator of by the conjugate of to make the denominator real.
Step 6.3.1.1.5
Multiply.
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Step 6.3.1.1.5.1
Combine.
Step 6.3.1.1.5.2
Simplify the numerator.
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Step 6.3.1.1.5.2.1
Apply the distributive property.
Step 6.3.1.1.5.2.2
Multiply by .
Step 6.3.1.1.5.2.3
Multiply by .
Step 6.3.1.1.5.3
Simplify the denominator.
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Step 6.3.1.1.5.3.1
Expand using the FOIL Method.
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Step 6.3.1.1.5.3.1.1
Apply the distributive property.
Step 6.3.1.1.5.3.1.2
Apply the distributive property.
Step 6.3.1.1.5.3.1.3
Apply the distributive property.
Step 6.3.1.1.5.3.2
Simplify.
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Step 6.3.1.1.5.3.2.1
Multiply by .
Step 6.3.1.1.5.3.2.2
Multiply by .
Step 6.3.1.1.5.3.2.3
Multiply by .
Step 6.3.1.1.5.3.2.4
Multiply by .
Step 6.3.1.1.5.3.2.5
Raise to the power of .
Step 6.3.1.1.5.3.2.6
Raise to the power of .
Step 6.3.1.1.5.3.2.7
Use the power rule to combine exponents.
Step 6.3.1.1.5.3.2.8
Add and .
Step 6.3.1.1.5.3.2.9
Add and .
Step 6.3.1.1.5.3.2.10
Add and .
Step 6.3.1.1.5.3.3
Simplify each term.
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Step 6.3.1.1.5.3.3.1
Rewrite as .
Step 6.3.1.1.5.3.3.2
Multiply by .
Step 6.3.1.1.5.3.4
Add and .
Step 6.3.1.1.6
Cancel the common factor of and .
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Step 6.3.1.1.6.1
Factor out of .
Step 6.3.1.1.6.2
Factor out of .
Step 6.3.1.1.6.3
Factor out of .
Step 6.3.1.1.6.4
Cancel the common factors.
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Step 6.3.1.1.6.4.1
Factor out of .
Step 6.3.1.1.6.4.2
Cancel the common factor.
Step 6.3.1.1.6.4.3
Rewrite the expression.
Step 6.3.1.1.7
Split the fraction into two fractions.
Step 6.3.1.1.8
Move the negative in front of the fraction.
Step 6.3.1.1.9
Multiply the numerator and denominator of by the conjugate of to make the denominator real.
Step 6.3.1.1.10
Multiply.
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Step 6.3.1.1.10.1
Combine.
Step 6.3.1.1.10.2
Simplify the numerator.
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Step 6.3.1.1.10.2.1
Apply the distributive property.
Step 6.3.1.1.10.2.2
Multiply by .
Step 6.3.1.1.10.2.3
Multiply .
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Step 6.3.1.1.10.2.3.1
Multiply by .
Step 6.3.1.1.10.2.3.2
Raise to the power of .
Step 6.3.1.1.10.2.3.3
Raise to the power of .
Step 6.3.1.1.10.2.3.4
Use the power rule to combine exponents.
Step 6.3.1.1.10.2.3.5
Add and .
Step 6.3.1.1.10.2.4
Simplify each term.
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Step 6.3.1.1.10.2.4.1
Rewrite as .
Step 6.3.1.1.10.2.4.2
Multiply by .
Step 6.3.1.1.10.3
Simplify the denominator.
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Step 6.3.1.1.10.3.1
Expand using the FOIL Method.
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Step 6.3.1.1.10.3.1.1
Apply the distributive property.
Step 6.3.1.1.10.3.1.2
Apply the distributive property.
Step 6.3.1.1.10.3.1.3
Apply the distributive property.
Step 6.3.1.1.10.3.2
Simplify.
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Step 6.3.1.1.10.3.2.1
Multiply by .
Step 6.3.1.1.10.3.2.2
Multiply by .
Step 6.3.1.1.10.3.2.3
Multiply by .
Step 6.3.1.1.10.3.2.4
Multiply by .
Step 6.3.1.1.10.3.2.5
Raise to the power of .
Step 6.3.1.1.10.3.2.6
Raise to the power of .
Step 6.3.1.1.10.3.2.7
Use the power rule to combine exponents.
Step 6.3.1.1.10.3.2.8
Add and .
Step 6.3.1.1.10.3.2.9
Add and .
Step 6.3.1.1.10.3.2.10
Add and .
Step 6.3.1.1.10.3.3
Simplify each term.
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Step 6.3.1.1.10.3.3.1
Rewrite as .
Step 6.3.1.1.10.3.3.2
Multiply by .
Step 6.3.1.1.10.3.4
Add and .
Step 6.3.1.1.11
Factor out of .
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Step 6.3.1.1.11.1
Factor out of .
Step 6.3.1.1.11.2
Factor out of .
Step 6.3.1.1.11.3
Factor out of .
Step 6.3.1.2
Combine the numerators over the common denominator.
Step 6.3.1.3
Simplify each term.
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Step 6.3.1.3.1
Apply the distributive property.
Step 6.3.1.3.2
Multiply by .
Step 6.3.1.3.3
Multiply by .
Step 6.3.1.3.4
Apply the distributive property.
Step 6.3.1.3.5
Multiply by .
Step 6.3.1.3.6
Multiply by .
Step 6.3.1.4
Simplify by adding terms.
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Step 6.3.1.4.1
Subtract from .
Step 6.3.1.4.2
Subtract from .
Step 6.3.1.5
Simplify each term.
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Step 6.3.1.5.1
Factor out of .
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Step 6.3.1.5.1.1
Factor out of .
Step 6.3.1.5.1.2
Factor out of .
Step 6.3.1.5.1.3
Factor out of .
Step 6.3.1.5.2
Cancel the common factor of and .
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Step 6.3.1.5.2.1
Factor out of .
Step 6.3.1.5.2.2
Cancel the common factors.
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Step 6.3.1.5.2.2.1
Factor out of .
Step 6.3.1.5.2.2.2
Cancel the common factor.
Step 6.3.1.5.2.2.3
Rewrite the expression.
Step 6.3.1.5.3
Move the negative in front of the fraction.
Step 6.3.1.6
Combine the numerators over the common denominator.
Step 6.3.2
Simplify the numerator.
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Step 6.3.2.1
Factor out of .
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Step 6.3.2.1.1
Factor out of .
Step 6.3.2.1.2
Factor out of .
Step 6.3.2.1.3
Factor out of .
Step 6.3.2.2
Apply the distributive property.
Step 6.3.2.3
Multiply by .
Step 6.3.3
Combine the numerators over the common denominator.
Step 6.3.4
Simplify the numerator.
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Step 6.3.4.1
Apply the distributive property.
Step 6.3.4.2
Simplify.
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Step 6.3.4.2.1
Multiply by .
Step 6.3.4.2.2
Multiply by .
Step 6.3.5
Simplify with factoring out.
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Step 6.3.5.1
Factor out of .
Step 6.3.5.2
Factor out of .
Step 6.3.5.3
Factor out of .
Step 6.3.5.4
Rewrite as .
Step 6.3.5.5
Factor out of .
Step 6.3.5.6
Factor out of .
Step 6.3.5.7
Factor out of .
Step 6.3.5.8
Simplify the expression.
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Step 6.3.5.8.1
Rewrite as .
Step 6.3.5.8.2
Move the negative in front of the fraction.